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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?

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Reni
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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? [#permalink] New post   26 Jul 2014, 09:59
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If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\) ?

A. 2
B. 4
C. 6
D. 14
E. 16­

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D
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Bunuel
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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? [#permalink] New post   26 Jul 2014, 10:09
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Reni wrote:
If x^2 + 1/x^2 =4, what is the value of x^4 + 1/x^4 ?

A. 2
B. 4
C. 6
D. 14
E. 16­


Squaring \(x^2 + \frac{1}{x^2} =4\) gives:

    \(x^4+2*x^2*\frac{1}{x^2}+\frac{1}{x^4}=16\);

    \(x^4+2+\frac{1}{x^4}=16\);

    \(x^4+\frac{1}{x^4}=14\)
.

Answer: D.­
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Re: If x^2 + 1/x^2 = 4, what is the value of [#permalink] New post   29 Oct 2023, 11:52
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yrozenblum wrote:
If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\)?

A. 2
B. 4
C. 6
D. 14
E. 16


Remember you can solve the question just by squaring both side and subtract -2

Will correspond to 14

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gmatophobia
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Re: If x^2 + 1/x^2 = 4, what is the value of [#permalink] New post   29 Oct 2023, 11:57
yrozenblum wrote:
If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\)?

A. 2
B. 4
C. 6
D. 14
E. 16


\(x^2 + \frac{1}{x^2} = 4\)

Squaring both sides we get

\((x^2)^2 + (\frac{1}{x^2})^2 + 2*x^2*\frac{1}{x^2} = (4)^2\)

\(x^4 + \frac{1}{x^4} + 2 = 16\)

\(x^4 + \frac{1}{x^4} = 16 - 2 = 14\)

Option D
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Bunuel
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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? [#permalink] New post   24 Feb 2024, 11:18
Expert Reply
 
Reni wrote:
If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\) ?

A. 2
B. 4
C. 6
D. 14
E. 16­

Show Spoiler
Attachment:
Screenshot 2024-02-24 at 16.19.52.png

­
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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? [#permalink]
24 Feb 2024, 11:18
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